What is the domain of f(x)=(sqrt(2+x))/(5-x) ?

The domain of f(x)=(sqrt(2+x))/(5-x) is -2 5

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domain of f(x)=(sqrt(2+x))/(5-x)

domain

f (x) = \frac{2 + x}{5 - x}

- 2 \leq x < 5 or x > 5

Interval Notation

[- 2, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

- 2 \leq x < 5 or x > 5

What is the domain of f(x)=(sqrt(2+x))/(5-x) ?
The domain of f(x)=(sqrt(2+x))/(5-x) is -2<= x<5\lor x>5